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# Cross product and torque

The cross product and the direction of torque. Created by Sal Khan.

## Want to join the conversation?

• I get the cross product, but it makes no sense that the torque is pointing out of the page if the object is rotating in the direction of the force, could someone explain? •   The unit vector given represents the axis of rotation about which the torque is acting.
• When I use the right hand rule, it points into the page for me. I did it exactly as he stated, rewatched his other videos, but I still don't really get it. I try pointing the first direction with my index, second with my middle, and I can get it pointing outwards, but it's very awkward for my right hand. Any advice? • I had the same problem but I think I've worked it out; when you point your index finger you have to make it so that you point it in the same direction as the vector i.e. your nail acts like the arrow head. Then if you do the same with your middle finger, you end up with a configuration wherein your thumb points outwards. What I (and I assume you) were doing was pointing the index finger the wrong way and this gets everything the wrong way round. I hope this made some sense!
• At Sal draws a circle and a dot in the centre to say that the vector is pointing out of the page, though what do you draw/signal to say that the vector pointing away from you? Thank you to whoever can answer this. • If the torque points away from you, or into the page, the convention is to draw a circle with an x through it. This is because the vector arrow of torque (or anything that requires the right hand rule) is typically thought of as a literal arrow, with a point on the front and feathers on the end. If the arrow were to approach you, you would only see the tip, which would look like a circle with a point in the center. If the arrow were flying away from you, it would appear to be a circle with a cross through it.
• It says that torque is perpendicular to radial distance and force, but may I ask why it is perpendicular? • If you have a force that is parallel to the radial distance you will not have any rotational force. All the force will contribute to tension or compression in the material. Any force that is not parallel to the radial vector will have a component that is perpendicular to the radial vector. This perpendicular force will cause the material to want to rotate in the direction of the perpendicular component. This is called a moment of force or torque. The cross product between 2 vectors, in this case radial vector cross with force vector, results in a third vector that is perpendicular to both the radial and the force vectors. Depending on which hand rule you use, the resulting torque could be into or out of the page.
• Why is Torque (T) = r x F and not F x r ? I understand that it will just change the direction and not the magnitude, but why does r come first. • Why does the vector have to be perpendicular the the direction of the force and the radius? And what is the "right hand rule"- how did he figure out if it is popping in or out? • How would torque work in three dimensions, say a F of (3,1,5)N acts on a point (7,3,1)m from the origin, what would be the torque on another point (0,10,0)? • I understand why torque points out of the page based on the right hand rule, but not from a conceptual sense. Its seems as if toque and force will point in the same direction since the arm rotates in a circle, and doesnt fly off the hinge. • I think partly the confusion comes from looking at torque as a kind of force--the torque pseudovector isn't pulling something in the same way that the force vector is, it's more of an axis of rotation. Remember, vectors don't need to apply a force, they just need to have a magnitude and direction; the weird thing about torque, as I understand it (and this may be wrong on a technicality but this is how it works in my head) is that the direction isn't constant--the torque causes spin around the vector in the "direction" we assign it.  